如何在博客园中插入公式

egin{align*}sin^2 A+sin^2B+sin^2C &=frac{1-cos 2A}{2}+frac{1-cos 2B}{2}+frac{1-cos 2C}{2}\ &=frac{3}{2}-frac{1}{2}(cos 2A+cos 2B+cos 2C)\ &=frac{3}{2}-cos(A+B)cos(A-B)-cos^2C+frac{1}{2}\ &=2+cos Ccos(A-B)-cos^2C \ &leq 2+|cos C|-cos^2C \ &=-(|cos C|-frac{1}{2})^2+frac{9}{4}\ &leq frac{9}{4}.end{align*}

egin{align}a^2+b^2&=c^2\eta^2&=sum_{n=0}^{infty}{frac{1}{n}}+int_0^1{frac{x}{e^x-1}dx}end{align}

{sigma}_{k}(n)=sum_{d|n}^{}{d}^{k}

egin{align}
  (a + b)^3  &= (a + b) (a + b)^2        \
             &= (a + b)(a^2 + 2ab + b^2) \
             &= a^3 + 3a^2b + 3ab^2 + b^3
end{align}

egin{flalign}
& q=
egin{cases}
    0 & mbox{ if $(A+B)mod 2 =0$}\ 第一个分支
    1 & mbox{ if $(A+B)mod 4 =0$};\ 第二个分支
    -1 & mbox{ if $(A-B)mod 2=0$}\ 第三个分支
end{cases}  & onumber
end{flalign}

egin{align}

E(S^2) &=Eleft(frac{1}{n} sum_{i=1}^n (X_i-ar{X})^2 ight) \ & =Eleft(frac{1}{n}sum_{i=1}^n X_i^2 ight) - Eleft(frac{1}{n}sum_{i=1}^n 2ar{X}X_i ight) + Eleft(frac{1}{n}sum_{i=1}^n ar{X}^2 ight) \ & =EX^2 -E(ar{X}^2) \ & =DX + (EX)^2 - Dar{X} - (Ear{X})^2 \ & =frac{n-1}{n}DX end{align}

egin{equation*}
  egin{rcase}
    B' &= -partial imes E          \
    E' &=  partial imes B - 4pi j \,
  end{rcase}
  quad ext {Maxwell's equations}
end{equation*}

egin{equation} egin{aligned}
  V_j &= v_j                      &
  X_i &= x_i - q_i x_j            &
      &= u_j + sum_{i e j} q_i \
  V_i &= v_i - q_i v_j            &
  X_j &= x_j                      &
  U_i &= u_i
end{aligned} end{equation}

egin{align*} f(x) & = (x+a)(x+b) \ & = x^2 + (a+b)x + ab end{align*}

egin{gather*} E(X)=lambda qquad D(X)=lambda \ E(ar{X})=lambda \ D(ar{X})=frac{lambda}{n} \ E(S^2)=frac{n-1}{n}lambda \ end{gather*}

egin{align*}sin^2 A+sin^2B+sin^2C &=frac{1-cos 2A}{2}+frac{1-cos 2B}{2}+frac{1-cos 2C}{2}\ &=frac{3}{2}-frac{1}{2}(cos 2A+cos 2B+cos 2C)\ &=frac{3}{2}-cos(A+B)cos(A-B)-cos^2C+frac{1}{2}\ &=2+cos Ccos(A-B)-cos^2C \ &leq 2+|cos C|-cos^2C \ &=-(|cos C|-frac{1}{2})^2+frac{9}{4}\ &leq frac{9}{4}.end{align*}

 

egin{align}a^2+b^2&=c^2\eta^2&=sum_{n=0}^{infty}{frac{1}{n}}+int_0^1{frac{x}{e^x-1}dx}end{align}

参考链接如下：
http://www.cnblogs.com/cmt/p/3279312.html#!comments
http://www.cnblogs.com/apprenticeship/p/4215755.html
http://www.cnblogs.com/cmt/p/markdown-latex.html
http://blog.sina.com.cn/s/blog_5e16f1770100gror.html